Question

Factor Which of the following is one of the factors?

Answer 1

There are multiple ways of answering this question. The first one is by factoring the given polynomial.

`x^2+3x-10=(x+5)(x-2)`

I got the factors by thinking of factors of -10 that add up to +3 (the ac Method). I thought of +5 and -2. They add up to +3 and their product is -10.

You can also use division, but that means you'll divide the trinomial by each of the choices until you get the one that does not have any remainders.

You may also try substituting the value of x into the trinomial. For example, to test if x + 5 is a factor, then equate it to zero. You will get:

`\begin{gathered} x+5=0 \\ x=-5 \end{gathered}`

Then, substitute -5 to all x's in x^2 + 3x - 10. If the answer is zero, then x + 5 is a factor of x^2 +3x - 10.

`\begin{gathered} (-5)^2+3(-5)-10 \\ =25-15-10 \\ =0 \end{gathered}`

Because the answer is zero, then x + 5 is a factor of x^2 +3x - 10.